Image Texture Darkens Entire Glass
There's still residual color information in the alpha area of your png. The better way to fix this is to get rid of the color mix node. Create a seperate shader for your screen-print ink material and wire that and your glass shader node into the mix shader node. Now drive the shader mix with your alpha channel.



This also allows you to modify the material properties of the ink without the need for a much more complex setup.



You could also achieve a result with minimal effort using the following node setup:



But this might not be physically correct, depending on the exact production method for the label, of course.